The spatial and temporal fluctuations occurring in an ensemble of cumulus clouds are modelled using three-dimensional Cloud Resolving Model (CRM) simulations of radiative-convective equilibrium, and are characterised theoretically using the approach of statistical mechanics. These cloud-scale fluctuations are not currently represented in convective parameterisation schemes, but may be relatively large if a scale separation does not exist between convective processes and the model resolution.

The spatial fluctuations within an idealised equilibrium ensemble of non-interacting clouds are characterised by analogy to the statistical mechanics analysis of an ideal gas system. An exponential distribution of cloud mass fluxes is predicted, as well as a quantitative form for the total mass flux probability distribution. The total mass flux variance is found to scale inversely with the mean number of clouds in the ensemble. The CRM provides validation of these predictions, although some spatial regularity is exhibited and attributed to direct convective interactions.

The fast time-scale of convective adjustment to equilibrium in response to externally imposed forcing perturbations is investigated both experimentally and theoretically. A ~1 hour convective response time is observed in CRM simulations, and is found to be linearly related to the mean cloud spacing of the initial state. A form of the Fluctuation-Dissipation theorem of non-equilibrium statistical mechanics is derived for the idealised convective system, and predicts an exact relation between the mass flux adjustment away from equilibrium and the autocorrelation of spontaneous fluctuations within the equilibrium state. The observed linear dependence of both quantities on cloud spacing in these experiments is taken as indirect validation of the theorem, although there are differences in the detailed structure.